Iterative Algorithms For Systems Of Variational Inequalities With Constraints Of Common Fixed Point

The system of variational inequalities is an important research direction in operations research and cybernetics.It has a wide range of applications in the fields of mixed optimization theory,differential equations,cybernetics and so on.One of the most common and important problems in the study of variational inequalities system is the iterative algorithm for solving the variational inequalities system constrained by common fixed point problems.This paper is divided into four parts.In Chapter 1,we introduce the background of the system of variational inequality,and briefly specify the main research achievements of the previous scholars and the main research work of this paper.In Chapter 2,we study the Mann viscosity extra-gradient method,and present a specific iterative algorithm to solve the corresponding variational inequality problem with common fixed point constraint,and prove the strong convergence of the algorithm.In Chapter 3,we introduce a new method for finding a common element of the variational inclusion and fixed point problem of an asymptotically nonexpansive mapping in a -uniformly smooth and uniformly convex Banach space.Under mild conditions,we prove the strong convergence of our algorithm by using gradient-projection method and the properties of asymptotically nonexpansive mapping.Our results improve and extend the corresponding ones announced by other authors in the very recent literature.In Chapter 4,we give the summary and the prospect of this paper.